Optimal local preparation of an arbitrary mixed state of two qubits. Closed expression for the single copy case

In this note we consider the problem of preparing a {\em single} copy of an arbitrary two-qubit mixed state $\rho$ starting from an entangled pure state $\psi$ and using only local operations assisted with classical communication. We present an analytical expression for the minimal amount of pure state entanglement required, and describe the corresponding local strategy. We also examine optimal probabilistic generalizations of the previous process.